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[en] Generalized permutation relation determined by a set of coefficients μ=(μ1,...,μsub(k)) are under consideration for a pair of operators a and a+ conjugated to each other. The totality of operator functions of a and a+ (the μ-algebra) is investigated. It is shown that a and a+ can be interpreted as the annihilation and creation operators of some 'particles'. Unlike the well known types of the quantization of Bose-Einstein and Fermi-Dirac the μ-quantization generally violates the proportionality between the energy of a state and its number of 'particles', a fact which is treated as a certain interaction between the 'particles'. All the particular cases of μ-quantization free from interaction are determined
[fr]On considere les relations de permutation generalisees determinees par un ensemble de coefficients μ=(μ1,...,μsub(k)), pour un couple d'operateurs a et a+ adjoints l'un de l'autre. On etudie les familles des operateurs (μ-algebres) fonctions de a et a+. Il est montre que a et a+ peuvent etre interpretes comme operateurs d'annihilation et de creation de certaines 'particules'. Contrairement aux types de quantification de Bose-Einstein et de Fermi-Dirac bien connus, la μ-quantification viole, en general, la proportionnalite entre l'energie d'un etat et son nombre de 'particules' ce qu'on peut interpreter comme une certaine interaction des 'particules'. Tous les cas particuliers de la μ-quantification, ou l'interaction n'a pas lieu, sont determines
[en] We study a coherent superposition ta+ra† of field annihilation and creation operators acting on continuous variable systems and propose its application for quantum state engineering. Specifically, it is investigated how the superposed operation transforms a classical state to a nonclassical one, together with emerging nonclassical effects. We also propose an experimental scheme to implement this elementary coherent operation and discuss its usefulness to produce an arbitrary superposition of number states involving up to two photons.
[en] With the help of the Drinfeld twist or factorizing F-matrix for the eight-vertex solid-on-solid (SOS) model, we find that in the F-basis provided by the twist the two sets of pseudo-particle creation operators simultaneously take completely symmetric and polarization free form. This allows us to obtain the explicit and completely symmetric expressions of the two sets of Bethe states of the model. (general)
[en] Using the underlying Lie-algebraical structure of a given number n of para-Fermi operators (PFO), the set of all finite dimensional representations of these operators is studied. The sub-space of all vacuum-like states is determined, i.e. vectors from the representation space on which the para-Fermi annihilation operators vanish. It is shown that this space carries an irreducible representation of the algebra SU(n). An explicit formula is written for the number of the linearly independent vacuum-like states which appear within an arbitrarily given irreducible representation of PFO, and their multiplicities are discussed. The results are compared with the corresponding ones obtained in the recent paper of Bracken and Green
[en] We solve the boson normal ordering problem for (q(a†)a + v(a†))n with arbitrary functions q(x) and v(x) and integer n, where a and a† are boson annihilation and creation operators, satisfying [a, a†] = 1. This consequently provides the solution for the exponential eλ(q(a†)a+v(a†)) generalizing the shift operator. In the course of these considerations we define and explore the monomiality principle and find its representations. We exploit the properties of Sheffer-type polynomials which constitute the inherent structure of this problem. In the end we give some examples illustrating the utility of the method and point out the relation to combinatorial structures
[en] For a general-form polarization biphoton qutrit, physically corresponding to a pair of arbitrarily polarized photons in a single frequency and wavevector mode, we explicitly find polarization Schmidt modes. A simple method is suggested for factorizing the state vector and the explicit expressions for the factorizing photon creation operators are found. The degrees of entanglement and polarization of a qutrit are shown to depend directly on the commutation features of the factorizing operators. Clear graphic representations for the Stokes vectors of the qutrit state as a whole, its Schmidt modes and factorizing single-photon creation operators are given based on the Poincaré sphere. An experimental scheme is proposed for measuring the parameters of the Schmidt decomposition as well as for demonstrating the operational meaning of qutrit entanglement. (paper)
[en] We have recently realized experimental schemes to implement the action of single-photon creation and annihilation operators onto completely classical and fully incoherent thermal light states (Parigi et al 2007 Science 317 1890). By applying alternated sequences of the creation and annihilation operators we observed that the resulting states depend on the order in which the two quantum operators are applied, thus obtaining the most direct experimental test of non-commutativity. Here we provide an extensive and detailed discussion of the main experimental issues related to the realization of these schemes.
[en] The construction of creation operators of exact strings in eigenvectors of the eight-vertex model at elliptic roots of unity of the crossing parameter which allow the generation of the complete set of degenerate eigenstates is based on the conjecture that the 'naive' string operator vanishes. In this paper, we present a proof of this conjecture. Furthermore, we show that for chains of odd length the string operator is either proportional to the symmetry operator S or vanishes depending on the precise form of the crossing parameter.
[en] In this paper we explore the possibility of creating the baryon asymmetry of the universe during inflation and reheating due to the decay of a field associated with the inflaton. CP violation is attained by assuming that this field is complex with a phase that varies as the inflaton evolves. We consider chaotic and natural inflation scenarios. In the former case, the complex decaying field is the inflaton itself and, in the latter case, the phase of the complex field is the inflaton. We calculate the asymmetry produced using the Bogolyubov formalism that relates annihilation and creation operators at late time to the annihilation and creation operators at early time